CatHDP2: Create objects of type "CatHDP2".

In bbricks: Bayesian Methods and Graphical Model Structures for Statistical Modeling

Description

Create an object of type "CatHDP2" that represents the Categorical-Hierarchical-Dirichlet-Process of two Dirichlet Process hierarchies, which is basically CatHDP with an additional layer of Dirichlet Process:

G |eta \sim DP(eta,U)

G_m|gamma \sim DP(gamma,G), m = 1:M

pi_{mj}|G_m,alpha \sim DP(alpha,G_m), j = 1:J_m

z|pi_{mj} \sim Categorical(pi_{mj})

k|z,G_m \sim Categorical(G_m), \textrm{ if z is a sample from the base measure }G_m

u|k,G \sim Categorical(G), \textrm{ if k is a sample from the base measure G}

where DP(eta,U) is a Dirichlet Process on positive integers, eta is the "concentration parameter", U is the "base measure" of this Dirichlet process, U is an uniform distribution on all positive integers. DP(gamma,G) is a Dirichlet Process on integers with concentration parameter gamma and base measure G. DP(alpha,G_m) is a Dirichlet Process on integers with concentration parameter alpha and base measure G_m. Categorical() is the Categorical distribution. See dCategorical for the definition of the Categorical distribution.
In the case of CatHDP2, u, z and k can only be positive integers.
This object will be used as a place for recording and accumulating information in the related inference/sampling functions such as posterior(), posteriorDiscard(), dPosteriorPredictive(), rPosteriorPredictive() and so on.

Usage

CatHDP2(
  objCopy = NULL,
  ENV = parent.frame(),
  gamma = list(eta = 1, gamma = 1, alpha = 1, m = 3, j = c(2, 3, 4))
)

Arguments

objCopy	an object of type "CatHDP2". If "objCopy" is not NULL, the function create a new "CatHDP2" object by copying the content from objCopy, otherwise this new object will be created by using "ENV" and "gamma". Default NULL.
ENV	environment, specify where the object will be created.
gamma	list, a named list of parameters, gamma=list(eta,gamma,alpha,m,j). Where gamma$eta is a numeric value specifying the concentration parameter of DP(eta,U), gamma$gamma is a numeric value specifying the concentration parameter of DP(gamma,G), gamma$alpha is a numeric value specifying the concentration parameter of DP(alpha,G_m), gamma$m is the number of groups M, gamma$j is the number of subgroups in each group, must satisfy length(gamma$j)=gamma$m.

Value

An object of class "CatHDP2".

References

Teh, Yee W., et al. "Sharing clusters among related groups: Hierarchical Dirichlet processes." Advances in neural information processing systems. 2005.

See Also

posterior.CatHDP2,posteriorDiscard.CatHDP2 ...

Examples

obj <- CatHDP2(gamma=list(eta=1,gamma=1,alpha=1,m=2,j=c(2,3)))
obj #print the content

bbricks documentation built on July 8, 2020, 7:29 p.m.